Finite Group Databasebeta

← C2×#11755061 #14480320

Subgroups — C2×#11755061 #14480320

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic, complemented
2C22×D5×#67C211yesmaximal, characteristic, complemented
3C2×#91828C211yesmaximal, characteristic, complemented
4C2×C5×#939C211yesmaximal, characteristic, complemented
5C2×#91577C211yesmaximal, characteristic, complemented
6C2×#91571C211yesmaximal, characteristic, complemented
7C2×#91569C211yesmaximal, characteristic, complemented
8C2×#91564C211yesmaximal, characteristic, complemented
9C2×#91563C211yesmaximal, characteristic, complemented
10C2×#91548C211yesmaximal, characteristic, complemented
11C22×#6665C211yesmaximal, characteristic, complemented
12#11755061C2116yesmaximal, direct product factor
13C2×#91474C211yesmaximal, characteristic, complemented
14C2×#91447C211yesmaximal, characteristic, complemented
15C2×#91407C211yesmaximal, characteristic, complemented
16C2×#91348C211yesmaximal, characteristic, complemented
17C2×#65939—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C24×C3×D5C2211yescharacteristic, complemented
20C23×D3×D5C2211yescharacteristic, complemented
21C22×C3×C5×D4C2211yescharacteristic, complemented
22C22×#1220C2211yescharacteristic, complemented
23C22×#1220C2211yescharacteristic, complemented
24C23×Dic15C2211yescharacteristic, complemented
25C22×C5×#67C2211yescharacteristic, complemented
26C22×C5×#67C2211yescharacteristic, complemented
27C23×C5×Dic3C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic
29C22×C3×C22⋊D5C2211yescharacteristic, complemented
30C2×C3×D4×D5—28no—
31C2×C3×D4×D5C2218yescomplemented
32C22×C3×D20C2211yescharacteristic
33C22×C3×C4×D5C2211yescharacteristic, complemented
34C2×D5×#67—28no—
35C2×D5×#67C2218yescomplemented
36C22×#1202C2211yescharacteristic
37C22×#1202C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic
39C22×#1201C2211yescharacteristic, complemented
40C22×D5×Dic3C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42#91828C2218yescomplemented
43C2×#6714C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C5×#939C2218yescomplemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
49#91577C2218yescomplemented
50#91571C2218yescomplemented
51#91569C2218yescomplemented
52#91564C2218yescomplemented
53#91563C2218yescomplemented
54#91548C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic, complemented
56C2×#6669C2211yescharacteristic, complemented
57C2×#6667C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic, complemented
60C2×#6665C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63C2×#6665C2211yescharacteristic, complemented
64C2×#6665C2211yescharacteristic, complemented
65C2×#6665C2218yescomplemented
66#91474C2218yescomplemented
67#91447C2218yescomplemented
68#91407C2218yescomplemented
69#91348C2218yescomplemented
70C2×#5804—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×D4×D5D311yescharacteristic, complemented
73C2×C5×#121—31no—
74C2×#4085—31no—
75C2×#4085—31no—
76C2×#4083—31no—
77C2×#4083—31no—
78C2×#4076—31no—
79C22×#685—31no—
80#65939—316no—
81C2×#4040—31no—
82C2×#4040—31no—
83C2×#4029—31no—
84C2×#4029—31no—
85C2×#4028—31no—
86C2×#4028—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5—24no—
92C23×C3×D5—42no—
93C23×C3×D5—42no—
94C23×C3×D5—42no—
95C23×C3×D5—42no—
96C23×C3×D5D418yescomplemented
97C23×C3×D5C2311yescharacteristic
98C23×C3×D5C2311yescharacteristic
99C23×C3×D5C2311yescharacteristic
100C23×C3×D5C2314yes—
101C23×C3×D5C2314yescomplemented
102C22×D3×D5—24no—
103C22×D3×D5—42no—
104C22×D3×D5—42no—
105C22×D3×D5C2314yescomplemented
106C2×C3×C5×D4—24no—
107C2×C3×C5×D4C2314yescomplemented
108C22×C3×C4×C5C2311yescharacteristic
109C2×#1220—24no—
110C2×#1220—42no—
111C2×#1220C2314yescomplemented
112C2×#1220C2314yescomplemented
113C22×Dic15—42no—
114C22×Dic15C2311yescharacteristic
115C22×Dic15C2311yescharacteristic
116C22×Dic15C2311yescharacteristic
117C22×Dic15C2314yescomplemented
118C2×C5×#67—24no—
119C2×C5×#67—42no—
120C2×C5×#67C2314yescomplemented
121C2×C5×#67C2314yescomplemented
122C22×C5×Dic3—42no—
123C22×C5×Dic3C2311yescharacteristic
124C22×C5×Dic3C2311yescharacteristic
125C22×C5×Dic3C2311yescharacteristic
126C22×C5×Dic3C2314yescomplemented
127C2×C3×C22⋊D5—24no—
128C2×C3×C22⋊D5—24no—
129C2×C3×C22⋊D5C2314yes—
130C2×C3×C22⋊D5C2314yescomplemented
131C22×C3×Dic5C2311yescharacteristic
132C3×D4×D5—232no—
133C2×C3×D20—24no—
134C2×C3×D20C2314yes—
135C2×C3×C4×D5—24no—
136C2×C3×C4×D5C2314yescomplemented
137D5×#67—232no—
138C2×#1202—24no—
139C2×#1202—42no—
140C2×#1202C2314yes—
141C2×#1202C2314yescomplemented
142C2×#1201—24no—
143C2×#1201—42no—
144C2×#1201C2314yes—
145C2×#1201C2314yescomplemented
146C2×D5×Dic3—24no—
147C2×D5×Dic3C2314yescomplemented
148#6719C2314yescomplemented
149#6714C2314yescomplemented
150#6712C2314yescomplemented
151C5×#217C2314yescomplemented
152C5×(C2×D3)⋊C4C2314yescomplemented
153C5×Dic3⋊C4C2314yescomplemented
154Dic3⋊Dic5C2314yescomplemented
155#6669C2314yescomplemented
156#6667C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158#6665C2314yescomplemented
159#6665C2314yescomplemented
160#6665C2314yescomplemented
161#6665C2314yescomplemented
162#6665C2314yescomplemented
163#6665C2314yescomplemented
164C23×C3×D4—51no—
165C23×#67—51no—
166C2×#953—51no—
167C2×#953—51no—
168C22×#217—51no—
169#5804—516no—
170C2×#939—51no—
171C2×#939—51no—
172C2×#939—51no—
173C2×#939D511yescharacteristic, complemented
174C2×#937—51no—
175C2×#937—51no—
176C2×#935—51no—
177C2×#935—51no—
178C2×#929—51no—
179C2×#929—51no—
180C24×D5—31no—
181C24×D5C2×D311yescharacteristic
182C24×D5C2×D311yescharacteristic, complemented
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C22×C5×D4C2×D311yescharacteristic, complemented
186C23×C4×C5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5C2×D311yescharacteristic
192C22×C22⋊D5C2×D311yescharacteristic, complemented
193C23×Dic5—31no—
194C2×D4×D5—28no—
195C2×D4×D5—38no—
196C2×D4×D5—68no—
197C2×D4×D5C2×D318yescomplemented
198C22×D20—31no—
199C22×D20—31no—
200C22×D20C2×D311yescharacteristic
201C22×C4×D5—31no—
202C22×C4×D5C2×D311yescharacteristic, complemented
203C5×#121—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4—31no—
207C2×C22⋊Dic5—31no—
208C2×C22⋊Dic5—31no—
209#4085—38no—
210#4085—38no—
211#4083—38no—
212#4083—38no—
213#4076—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—38no—
221C2×#685—31no—
222C2×#685—31no—
223C2×C4⋊Dic5—31no—
224C2×#683—31no—
225C2×#683—31no—
226#4040—38no—
227#4040—38no—
228#4029—38no—
229#4029—38no—
230#4028—38no—
231#4028—38no—
232C2×#534—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5—22no—
237C23×C3×C5—22no—
238C23×C3×C5C2×D414yes—
239C23×C3×C5C2412yes—
240C23×C3×C5C2412yes—
241C23×C3×C5C2411yescharacteristic
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15C2412yes—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3C2412yes—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5—22no—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—28no—
258C22×C3×D5—416no—
259C22×C3×D5—44no—
260C22×C3×D5—44no—
261C22×C3×D5—44no—
262C22×C3×D5—44no—
263C22×C3×D5—416no—
264C22×C3×D5C2×D414yes—
265C22×C3×D5C2×D414yes—
266C22×C3×D5C2×D4116yescomplemented
267C22×C3×D5C2412yes—
268C22×C3×D5C2412yes—
269C22×C3×D5C2412yes—
270C2×D3×D5—28no—
271C2×D3×D5—44no—
272C2×D3×D5—44no—
273C2×D3×D5—416no—
274C3×C5×D4—28no—
275C2×C3×C4×C5—22no—
276C2×C3×C4×C5C2412yes—
277#1220—28no—
278#1220—44no—
279C2×Dic15—22no—
280C2×Dic15—22no—
281C2×Dic15—22no—
282C2×Dic15—44no—
283C2×Dic15C2412yes—
284C2×Dic15C2412yes—
285C2×Dic15C2412yes—
286C5×#67—28no—
287C5×#67—44no—
288C2×C5×Dic3—22no—
289C2×C5×Dic3—22no—
290C2×C5×Dic3—22no—
291C2×C5×Dic3—44no—
292C2×C5×Dic3C2412yes—
293C2×C5×Dic3C2412yes—
294C2×C5×Dic3C2412yes—
295C3×C22⋊D5—28no—
296C3×C22⋊D5—28no—
297C2×C3×Dic5—22no—
298C2×C3×Dic5C2412yes—
299C3×D20—28no—
300C3×C4×D5—28no—
301#1202—28no—
302#1202—44no—
303#1201—28no—
304#1201—44no—
305D5×Dic3—28no—
306C25×C3—51no—
307C25×C3—51no—
308C24×D3—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4—58no—
312C22×C3×D4—51no—
313C22×C3×D4—108no—
314C22×C3×D4C2×D511yescharacteristic, complemented
315C23×C3×C4—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67—51no—
320C22×#67—58no—
321C22×#67—51no—
322C22×#67—51no—
323C22×#67—108no—
324C22×#67C2×D511yescharacteristic, complemented
325C22×#67C2×D511yescharacteristic, complemented
326C23×Dic3—51no—
327C23×Dic3—51no—
328C23×Dic3C2×D511yescharacteristic, complemented
329#953—58no—
330#953—58no—
331C2×#217—51no—
332C2×#217—51no—
333C2×#217—51no—
334C2×#217—51no—
335C2×#217—51no—
336C2×#217—51no—
337C2×#217—51no—
338C2×#217—58no—
339C2×#217C2×D511yescharacteristic, complemented
340#939—58no—
341#939—58no—
342#939—58no—
343#939C2×D518yescomplemented
344#937—58no—
345#937—58no—
346#935—58no—
347#935—58no—
348#929—58no—
349#929—58no—
350C2×(C2×D3)⋊C4—51no—
351C2×(C2×D3)⋊C4—51no—
352C2×(C2×D3)⋊C4—51no—
353C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
354C2×Dic3⋊C4—51no—
355C2×Dic3⋊C4—51no—
356C2×Dic3⋊C4—51no—
357C2×Dic3⋊C4C2×D511yescharacteristic, complemented
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C24×C5C22×D311yescharacteristic
361C23×D5—24no—
362C23×D5—31no—
363C23×D5—34no—
364C23×D5—42no—
365C23×D5—42no—
366C23×D5—42no—
367C23×D5—42no—
368C23×D5—64no—
369C23×D5—122no—
370C23×D5—122no—
371C23×D5#6718yescomplemented
372C23×D5C22×D311yescharacteristic
373C23×D5C22×D311yescharacteristic
374C23×D5C22×D311yescharacteristic
375C23×D5C22×D314yes—
376C23×D5C22×D314yescomplemented
377C2×C5×D4—24no—
378C2×C5×D4—34no—
379C2×C5×D4—34no—
380C2×C5×D4—64no—
381C2×C5×D4—122no—
382C2×C5×D4C22×D314yescomplemented
383C22×C4×C5—31no—
384C22×C4×C5—31no—
385C22×C4×C5—31no—
386C22×C4×C5—34no—
387C22×C4×C5—122no—
388C22×C4×C5C22×D311yescharacteristic
389C2×C22⋊D5—24no—
390C2×C22⋊D5—24no—
391C2×C22⋊D5—34no—
392C2×C22⋊D5—34no—
393C2×C22⋊D5—34no—
394C2×C22⋊D5—34no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—64no—
397C2×C22⋊D5—122no—
398C2×C22⋊D5—122no—
399C2×C22⋊D5C22×D314yes—
400C2×C22⋊D5C22×D314yescomplemented
401C22×Dic5—31no—
402C22×Dic5—31no—
403C22×Dic5—31no—
404C22×Dic5—34no—
405C22×Dic5—122no—
406C22×Dic5C22×D311yescharacteristic
407D4×D5—232no—
408D4×D5—632no—
409C2×D20—24no—
410C2×D20—34no—
411C2×D20—34no—
412C2×D20—64no—
413C2×D20—122no—
414C2×D20C22×D314yes—
415C2×C4×D5—24no—
416C2×C4×D5—34no—
417C2×C4×D5—64no—
418C2×C4×D5C22×D314yescomplemented
419C5×C4⋊C4—34no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C22⋊Dic5—34no—
423C22⋊Dic5—34no—
424#685—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431#685—34no—
432C4⋊Dic5—34no—
433#683—34no—
434#683—34no—
435C23×D4—51no—
436C23×D4—151no—
437#534—1516no—
438C2×#123—151no—
439C2×#123—151no—
440C2×#123—151no—
441C2×#123—151no—
442C2×#121—31no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#121—151no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#120—151no—
450C22×C22⋊C4—151no—
451C22×C3×C5—28no—
452C22×C3×C5—22no—
453C22×C3×C5—22no—
454C22×C3×C5—22no—
455C22×C3×C5—22no—
456C22×C3×C5—22no—
457C22×C3×C5—44no—
458C22×C3×C5C22×D414yes—
459C22×C3×C5C22×D412yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5H(5,𝔽2)12yes—
462C22×C3×C5C2511yescharacteristic
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—44no—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—22no—
470C2×C5×D3—44no—
471C2×C3×D5—28no—
472C2×C3×D5—28no—
473C2×C3×D5—22no—
474C2×C3×D5—22no—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—416no—
481C2×C3×D5—416no—
482C2×C3×D5—44no—
483C2×C3×D5C22×D414yes—
484C2×C3×D5C22×D414yes—
485D3×D5—416no—
486C3×C4×C5—22no—
487Dic15—22no—
488Dic15—22no—
489Dic15—22no—
490C3×Dic5—22no—
491C5×Dic3—22no—
492C5×Dic3—22no—
493C5×Dic3—22no—
494C24×C3—51no—
495C24×C3—51no—
496C24×C3—58no—
497C24×C3—54no—
498C24×C3—51no—
499C24×C3—54no—
500C24×C3—104no—
501C24×C3—202no—
502C24×C3—202no—
503C24×C3—202no—
504C24×C3—202no—
505C24×C3C22×D511yescharacteristic
506C24×C3C22×D511yescharacteristic
507C23×D3—51no—
508C23×D3—54no—
509C23×D3—104no—
510C23×D3—202no—
511C23×D3—202no—
512C23×D3C22×D511yescharacteristic
513C2×C3×D4—24no—
514C2×C3×D4—54no—
515C2×C3×D4—54no—
516C2×C3×D4—54no—
517C2×C3×D4—104no—
518C2×C3×D4—1032no—
519C2×C3×D4—104no—
520C2×C3×D4—104no—
521C2×C3×D4C22×D514yescomplemented
522C22×C3×C4—51no—
523C22×C3×C4—54no—
524C22×C3×C4—104no—
525C22×C3×C4C22×D511yescharacteristic
526C2×#67—24no—
527C2×#67—42no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—54no—
531C2×#67—54no—
532C2×#67—54no—
533C2×#67—54no—
534C2×#67—104no—
535C2×#67—1032no—
536C2×#67—104no—
537C2×#67—104no—
538C2×#67—202no—
539C2×#67—202no—
540C2×#67—202no—
541C2×#67C22×D514yescomplemented
542C2×#67C22×D514yescomplemented
543C22×Dic3—42no—
544C22×Dic3—51no—
545C22×Dic3—51no—
546C22×Dic3—51no—
547C22×Dic3—54no—
548C22×Dic3—54no—
549C22×Dic3—104no—
550C22×Dic3—202no—
551C22×Dic3C22×D511yescharacteristic
552C22×Dic3C22×D511yescharacteristic
553C22×Dic3C22×D511yescharacteristic
554C22×Dic3C22×D514yescomplemented
555#217—54no—
556#217—54no—
557#217—54no—
558#217—54no—
559#217—54no—
560#217—54no—
561#217—54no—
562#217C22×D514yescomplemented
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4—54no—
566(C2×D3)⋊C4C22×D514yescomplemented
567Dic3⋊C4—54no—
568Dic3⋊C4—54no—
569Dic3⋊C4—54no—
570Dic3⋊C4C22×D514yescomplemented
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—32no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5C2×#6714yes—
581C23×C5C23×D312yes—
582C23×C5C23×D312yes—
583C23×C5C23×D311yescharacteristic
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—22no—
588C22×D5—22no—
589C22×D5—22no—
590C22×D5—22no—
591C22×D5—28no—
592C22×D5—32no—
593C22×D5—416no—
594C22×D5—44no—
595C22×D5—44no—
596C22×D5—44no—
597C22×D5—44no—
598C22×D5—416no—
599C22×D5—62no—
600C22×D5—62no—
601C22×D5—62no—
602C22×D5—68no—
603C22×D5—124no—
604C22×D5—124no—
605C22×D5—1216no—
606C22×D5C2×#6714yes—
607C22×D5C2×#6714yes—
608C22×D5C2×#67116yescomplemented
609C22×D5C23×D312yes—
610C22×D5C23×D312yes—
611C22×D5C23×D312yes—
612C5×D4—28no—
613C5×D4—68no—
614C5×D4—124no—
615C2×C4×C5—22no—
616C2×C4×C5—32no—
617C2×C4×C5—32no—
618C2×C4×C5—32no—
619C2×C4×C5—62no—
620C2×C4×C5—62no—
621C2×C4×C5—62no—
622C2×C4×C5—124no—
623C2×C4×C5C23×D312yes—
624C22⋊D5—28no—
625C22⋊D5—28no—
626C22⋊D5—68no—
627C22⋊D5—68no—
628C22⋊D5—124no—
629C22⋊D5—124no—
630C2×Dic5—22no—
631C2×Dic5—32no—
632C2×Dic5—32no—
633C2×Dic5—32no—
634C2×Dic5—62no—
635C2×Dic5—62no—
636C2×Dic5—62no—
637C2×Dic5—124no—
638C2×Dic5C23×D312yes—
639D20—28no—
640D20—68no—
641D20—124no—
642C4×D5—28no—
643C4×D5—68no—
644C25—51no—
645C25—51no—
646C25—151no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—58no—
652C22×D4—51no—
653C22×D4—108no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—31no—
664C23×C4—51no—
665C23×C4—151no—
666C23×C4—151no—
667#123—158no—
668#123—158no—
669#123—158no—
670#123—158no—
671#121—38no—
672#121—158no—
673#121—158no—
674#121—158no—
675#120—158no—
676#120—158no—
677#120—158no—
678#120—158no—
679C2×C4⋊C4—31no—
680C2×C4⋊C4—151no—
681C2×C4⋊C4—151no—
682C2×C4⋊C4—151no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—31no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4—158no—
691C2×C22⋊C4—151no—
692C2×C22⋊C4—151no—
693C2×C22⋊C4—151no—
694C2×C22⋊C4—151no—
695C2×C22⋊C4—151no—
696C2×C3×C5—24no—
697C2×C3×C5—42no—
698C2×C3×C5#53414yescomplemented
699C2×C3×C5C23×D411yescharacteristic
700C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
701C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
702D15—42no—
703C3×D5—24no—
704C3×D5—24no—
705C3×D5—42no—
706C5×D3—42no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—22no—
711C23×C3—22no—
712C23×C3—54no—
713C23×C3—54no—
714C23×C3—52no—
715C23×C3—52no—
716C23×C3—516no—
717C23×C3—52no—
718C23×C3—108no—
719C23×C3—102no—
720C23×C3—102no—
721C23×C3—102no—
722C23×C3—102no—
723C23×C3—102no—
724C23×C3—102no—
725C23×C3—102no—
726C23×C3—2016no—
727C23×C3—204no—
728C23×C3—204no—
729C23×C3—204no—
730C23×C3—204no—
731C23×C3—2016no—
732C23×C3D4×D514yes—
733C23×C3C23×D512yes—
734C23×C3C23×D512yes—
735C23×C3C23×D511yescharacteristic
736C22×D3—22no—
737C22×D3—22no—
738C22×D3—22no—
739C22×D3—52no—
740C22×D3—108no—
741C22×D3—102no—
742C22×D3—102no—
743C22×D3—102no—
744C22×D3—204no—
745C22×D3—204no—
746C22×D3—2016no—
747C22×D3C23×D512yes—
748C3×D4—28no—
749C3×D4—108no—
750C3×D4—108no—
751C3×D4—108no—
752C2×C3×C4—22no—
753C2×C3×C4—52no—
754C2×C3×C4—108no—
755C2×C3×C4—102no—
756C2×C3×C4C23×D512yes—
757#67—28no—
758#67—44no—
759#67—108no—
760#67—108no—
761#67—108no—
762#67—204no—
763#67—204no—
764#67—204no—
765C2×Dic3—22no—
766C2×Dic3—22no—
767C2×Dic3—22no—
768C2×Dic3—44no—
769C2×Dic3—52no—
770C2×Dic3—52no—
771C2×Dic3—52no—
772C2×Dic3—108no—
773C2×Dic3—102no—
774C2×Dic3—102no—
775C2×Dic3—102no—
776C2×Dic3—204no—
777C2×Dic3C23×D512yes—
778C2×Dic3C23×D512yes—
779C2×Dic3C23×D512yes—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—28no—
783C22×C5—22no—
784C22×C5—22no—
785C22×C5—22no—
786C22×C5—44no—
787C22×C5—62no—
788C22×C5—62no—
789C22×C5—62no—
790C22×C5—124no—
791C22×C5#100412yes—
792C22×C5#100412yes—
793C22×C5C22×#6714yes—
794C22×C5C22×#6712yes—
795C22×C5C24×D311yescharacteristic
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—28no—
801C2×D5—28no—
802C2×D5—22no—
803C2×D5—22no—
804C2×D5—22no—
805C2×D5—416no—
806C2×D5—416no—
807C2×D5—44no—
808C2×D5—62no—
809C2×D5—62no—
810C2×D5—62no—
811C2×D5—1216no—
812C2×D5—124no—
813C2×D5C22×#6714yes—
814C2×D5C22×#6714yes—
815C4×C5—22no—
816C4×C5—62no—
817C4×C5—62no—
818C4×C5—62no—
819Dic5—22no—
820Dic5—62no—
821Dic5—62no—
822Dic5—62no—
823C24—31no—
824C24—51no—
825C24—51no—
826C24—58no—
827C24—54no—
828C24—51no—
829C24—54no—
830C24—104no—
831C24—154no—
832C24—151no—
833C24—202no—
834C24—202no—
835C24—202no—
836C24—202no—
837C24—304no—
838C24—602no—
839C24—602no—
840C24C2×D3×D511yescharacteristic
841C24C2×D3×D511yescharacteristic
842C2×D4—24no—
843C2×D4—34no—
844C2×D4—34no—
845C2×D4—54no—
846C2×D4—54no—
847C2×D4—54no—
848C2×D4—64no—
849C2×D4—104no—
850C2×D4—1032no—
851C2×D4—104no—
852C2×D4—104no—
853C2×D4—122no—
854C2×D4—154no—
855C2×D4—154no—
856C2×D4—154no—
857C2×D4—154no—
858C2×D4—154no—
859C2×D4—154no—
860C2×D4—304no—
861C2×D4—3032no—
862C2×D4—304no—
863C2×D4—304no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C2×D4C2×D3×D514yescomplemented
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—34no—
872C22×C4—51no—
873C22×C4—54no—
874C22×C4—104no—
875C22×C4—122no—
876C22×C4—154no—
877C22×C4—151no—
878C22×C4—151no—
879C22×C4—151no—
880C22×C4—154no—
881C22×C4—304no—
882C22×C4—602no—
883C22×C4C2×D3×D511yescharacteristic
884C4⋊C4—34no—
885C4⋊C4—154no—
886C4⋊C4—154no—
887C4⋊C4—154no—
888C22⋊C4—34no—
889C22⋊C4—34no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4—154no—
893C22⋊C4—154no—
894C22⋊C4—154no—
895C22⋊C4—154no—
896C22⋊C4—154no—
897C22⋊C4—154no—
898C22⋊C4—154no—
899C22⋊C4—154no—
900C3×C5C2×#53411yescharacteristic, complemented, Hall
901C22×C3—28no—
902C22×C3—22no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—22no—
907C22×C3—44no—
908C22×C3—54no—
909C22×C3—54no—
910C22×C3—108no—
911C22×C3—108no—
912C22×C3—102no—
913C22×C3—102no—
914C22×C3—102no—
915C22×C3—102no—
916C22×C3—102no—
917C22×C3—102no—
918C22×C3—102no—
919C22×C3—2016no—
920C22×C3—2016no—
921C22×C3—204no—
922C22×C3C2×D4×D514yes—
923C22×C3C2×D4×D512yes—
924C22×C3#414412yes—
925C22×C3#414912yes—
926C22×C3C24×D511yescharacteristic
927C2×D3—22no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—44no—
931C2×D3—102no—
932C2×D3—102no—
933C2×D3—102no—
934C2×D3—2016no—
935C2×D3—204no—
936C3×C4—22no—
937C3×C4—102no—
938Dic3—22no—
939Dic3—22no—
940Dic3—22no—
941Dic3—102no—
942Dic3—102no—
943Dic3—102no—
944C2×C5—24no—
945C2×C5—42no—
946C2×C5—122no—
947C2×C5#580414yescomplemented
948C2×C5C2×#100411yescharacteristic
949C2×C5C2×#100411yescharacteristic
950C2×C5C23×#6711yescharacteristic
951D5—24no—
952D5—24no—
953D5—42no—
954D5—122no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—32no—
961C23—54no—
962C23—54no—
963C23—52no—
964C23—52no—
965C23—516no—
966C23—52no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—108no—
971C23—102no—
972C23—102no—
973C23—102no—
974C23—102no—
975C23—102no—
976C23—102no—
977C23—102no—
978C23—152no—
979C23—2016no—
980C23—204no—
981C23—204no—
982C23—204no—
983C23—204no—
984C23—2016no—
985C23—308no—
986C23—302no—
987C23—302no—
988C23—302no—
989C23—604no—
990C23—604no—
991C23—6016no—
992C23D5×#6714yes—
993C23C22×D3×D512yes—
994C23C22×D3×D512yes—
995C23C22×D3×D511yescharacteristic
996D4—28no—
997D4—68no—
998D4—108no—
999D4—108no—
1000D4—108no—
1001D4—124no—
1002D4—308no—
1003D4—308no—
1004D4—308no—
1005D4—604no—
1006D4—604no—
1007D4—604no—
1008C2×C4—22no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—52no—
1013C2×C4—62no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—108no—
1017C2×C4—102no—
1018C2×C4—124no—
1019C2×C4—152no—
1020C2×C4—152no—
1021C2×C4—152no—
1022C2×C4—308no—
1023C2×C4—302no—
1024C2×C4—302no—
1025C2×C4—302no—
1026C2×C4—604no—
1027C2×C4C22×D3×D512yes—
1028C2×C3—24no—
1029C2×C3—42no—
1030C2×C3—104no—
1031C2×C3—104no—
1032C2×C3—202no—
1033C2×C3#6593914yescomplemented
1034C2×C3C22×D4×D511yescharacteristic
1035C2×C3C2×#414411yescharacteristic
1036C2×C3C2×#414911yescharacteristic
1037D3—42no—
1038D3—202no—
1039C5C2×#580411yescharacteristic, complemented, Sylow
1040C22—28no—
1041C22—22no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—44no—
1047C22—54no—
1048C22—54no—
1049C22—62no—
1050C22—62no—
1051C22—62no—
1052C22—108no—
1053C22—108no—
1054C22—102no—
1055C22—102no—
1056C22—102no—
1057C22—102no—
1058C22—102no—
1059C22—102no—
1060C22—102no—
1061C22—124no—
1062C22—2016no—
1063C22—2016no—
1064C22—204no—
1065C22—302no—
1066C22—302no—
1067C22—302no—
1068C22—6016no—
1069C22—604no—
1070C22#9202512yes—
1071C22#9202612yes—
1072C22C2×D5×#6714yes—
1073C22C2×D5×#6712yes—
1074C22C23×D3×D511yescharacteristic
1075C4—22no—
1076C4—62no—
1077C4—62no—
1078C4—62no—
1079C4—102no—
1080C4—302no—
1081C4—302no—
1082C4—302no—
1083C3C2×#6593911yescharacteristic, complemented, Sylow
1084C2—24no—
1085C2—42no—
1086C2—104no—
1087C2—104no—
1088C2—122no—
1089C2—202no—
1090C2—602no—
1091C2#1175506114yesdirect product factor
1092C2C2×#9202511yescharacteristic
1093C2C2×#9202611yescharacteristic
1094C2C22×D5×#6711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#534
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×D4×D5C2semidirect
2. C22×D5×#67C2semidirect
3. C2×#91828C2semidirect
4. C2×C5×#939C2semidirect
5. C2×#91577C2semidirect
6. C2×#91571C2semidirect
7. C2×#91569C2semidirect
8. C2×#91564C2semidirect
9. C2×#91563C2semidirect
10. C2×#91548C2semidirect
11. C22×#6665C2semidirect
12. #11755061C2direct (N × H)
13. C2×#91474C2semidirect
14. C2×#91447C2semidirect
15. C2×#91407C2semidirect
16. C2×#91348C2semidirect
19. C24×C3×D5C22semidirect
20. C23×D3×D5C22semidirect
21. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
23. C22×#1220C22semidirect
24. C23×Dic15C22semidirect
25. C22×C5×#67C22semidirect
26. C22×C5×#67C22semidirect
27. C23×C5×Dic3C22semidirect
29. C22×C3×C22⋊D5C22semidirect
31. C2×C3×D4×D5C22semidirect
33. C22×C3×C4×D5C22semidirect
35. C2×D5×#67C22semidirect
37. C22×#1202C22semidirect
39. C22×#1201C22semidirect
40. C22×D5×Dic3C22semidirect
41. C2×#6719C22semidirect
42. #91828C22semidirect
43. C2×#6714C22semidirect
44. C2×#6712C22semidirect
45. C2×C5×#217C22semidirect
46. C5×#939C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×Dic3⋊C4C22semidirect
49. #91577C22semidirect
50. #91571C22semidirect
51. #91569C22semidirect
52. #91564C22semidirect
53. #91563C22semidirect
54. #91548C22semidirect
55. C2×Dic3⋊Dic5C22semidirect
56. C2×#6669C22semidirect
57. C2×#6667C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
59. C2×#6665C22semidirect
60. C2×#6665C22semidirect
61. C2×#6665C22semidirect
62. C2×#6665C22semidirect
63. C2×#6665C22semidirect
64. C2×#6665C22semidirect
65. C2×#6665C22semidirect
66. #91474C22semidirect
67. #91447C22semidirect
68. #91407C22semidirect
69. #91348C22semidirect
72. C22×D4×D5D3semidirect
96. C23×C3×D5D4semidirect
101. C23×C3×D5C23semidirect
105. C22×D3×D5C23semidirect
107. C2×C3×C5×D4C23semidirect
111. C2×#1220C23semidirect
112. C2×#1220C23semidirect
117. C22×Dic15C23semidirect
120. C2×C5×#67C23semidirect
121. C2×C5×#67C23semidirect
126. C22×C5×Dic3C23semidirect
130. C2×C3×C22⋊D5C23semidirect
136. C2×C3×C4×D5C23semidirect
141. C2×#1202C23semidirect
145. C2×#1201C23semidirect
147. C2×D5×Dic3C23semidirect
148. #6719C23semidirect
149. #6714C23semidirect
150. #6712C23semidirect
151. C5×#217C23semidirect
152. C5×(C2×D3)⋊C4C23semidirect
153. C5×Dic3⋊C4C23semidirect
154. Dic3⋊Dic5C23semidirect
155. #6669C23semidirect
156. #6667C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. #6665C23semidirect
161. #6665C23semidirect
162. #6665C23semidirect
163. #6665C23semidirect
173. C2×#939D5semidirect
182. C24×D5C2×D3semidirect
185. C22×C5×D4C2×D3semidirect
192. C22×C22⋊D5C2×D3semidirect
197. C2×D4×D5C2×D3semidirect
202. C22×C4×D5C2×D3semidirect
266. C22×C3×D5C2×D4semidirect
314. C22×C3×D4C2×D5semidirect
324. C22×#67C2×D5semidirect
325. C22×#67C2×D5semidirect
328. C23×Dic3C2×D5semidirect
339. C2×#217C2×D5semidirect
343. #939C2×D5semidirect
353. C2×(C2×D3)⋊C4C2×D5semidirect
357. C2×Dic3⋊C4C2×D5semidirect
371. C23×D5#67semidirect
376. C23×D5C22×D3semidirect
382. C2×C5×D4C22×D3semidirect
400. C2×C22⋊D5C22×D3semidirect
418. C2×C4×D5C22×D3semidirect
521. C2×C3×D4C22×D5semidirect
541. C2×#67C22×D5semidirect
542. C2×#67C22×D5semidirect
554. C22×Dic3C22×D5semidirect
562. #217C22×D5semidirect
566. (C2×D3)⋊C4C22×D5semidirect
570. Dic3⋊C4C22×D5semidirect
608. C22×D5C2×#67semidirect
662. C22×D4D3×D5semidirect
698. C2×C3×C5#534semidirect
867. C2×D4C2×D3×D5semidirect
900. C3×C5C2×#534semidirect
947. C2×C5#5804semidirect
1033. C2×C3#65939semidirect
1039. C5C2×#5804semidirect
1083. C3C2×#65939semidirect
1091. C2#11755061direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×D4×D52
C22×D5×#672
C2×#918282
C2×C5×#9392
C2×#915772
C2×#915712
C2×#915692
C2×#915642
C2×#915632
C2×#915482
C22×#66652
#117550612
C2×#914742
C2×#914472
C2×#914072
C2×#913482
C2×#659393
C2×#58045